Question

Lungimile laturilor unui triunghi sunt direct proporționale cu numerele 3, 4 şi 6. Produsul lungimilor laturilor triunghiului este egal cu 576cm la a 3-ea.Să se afle lungimile laturilor triunghiului.​

Answer 1

 

$\displaystyle\bf\\a, b, c~~dp~cu~3;4;6\\\\\frac{a}{3}=\frac{b}{4}=\frac{c}{6}=k\\\\a=3k\\b=4k\\c=6k\\\\a\times b\times c=576\\\\3k\times 4k\times6k=576\\\\3\times 4\times6\times k^3=576\\\\72k^3=576\\\\k^3=\frac{576}{72}\\\\k^3=8\\\\k=\sqrt[\b3]{\bf8}\\\\\boxed{\bf k=2}\\\\a=3k=3\times2=6\\b=4k=4\times2=8\\c=6k=6\times2=12$